A systematic approach for modeling a nonlocal eddy diffusivity

TL;DR

This paper introduces a cost-effective systematic method for modeling nonlocal eddy diffusivities in passive scalar transport, using matched moment inverse operators to improve mean field models while maintaining computational efficiency.

Contribution

It develops a systematic approach employing matched moment inverse operators to model nonlocal eddy diffusivities efficiently, bridging the gap between accuracy and computational cost.

Findings

The method captures leading-order nonlocal effects in eddy diffusivities.

Models are expressed as PDEs, making them compatible with existing CFD tools.

Improved accuracy over Boussinesq-limit models in mean field transport.

Abstract

This study considers advective and diffusive transport of passive scalar fields by spatially-varying incompressible flows. Prior studies have shown that the eddy diffusivities governing the mean field transport in such systems can generally be nonlocal in space and time. While for many flows nonlocal eddy diffusivities are more accurate than commonly-used Boussinesq eddy diffusivities, nonlocal eddy diffusivities are often computationally cost-prohibitive to obtain and difficult to implement in practice. We develop a systematic and more cost-effective approach for modeling nonlocal eddy diffusivities using matched moment inverse (MMI) operators. These operators are constructed using only a few leading-order moments of the exact nonlocal eddy diffusivity kernel, which can be easily computed using the inverse macroscopic forcing method (IMFM) (Mani and Park (2021)). The resulting reduced-order models for the mean fields that incorporate the modeled eddy diffusivities often improve Boussinesq-limit models since they capture leading-order nonlocal effects. But more importantly, these models can be expressed as partial differential equations that are readily solvable using existing computational fluid dynamics capabilities rather than as integro-partial differential equations.